Integration of (3x+4)^2
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respect to x
∫
(
3
x
+
4
)
2
d
x
Let
u
=
3
x
+
4
. Then
d
u
=
3
d
x
, so
1
3
d
u
=
d
x
. Rewrite using
u
and
d
u
.
Let
u
=
3
x
+
4
. Find
d
u
d
x
.
3
1
Divide
3
by
1
.
3
Rewrite the problem using
u
and
d
u
.
∫
u
2
1
3
d
u
Combine
u
2
and
1
3
.
∫
u
2
3
d
u
Since
1
3
is constant with respect to
u
, move
1
3
out of the integral.
1
3
∫
u
2
d
u
By the Power Rule, the integral of
u
2
with respect to
u
is
1
3
u
3
.
1
3
(
1
3
u
3
+
C
)
Simplify.
Simplify.
1
3
(
1
3
u
3
)
+
C
Combine fractions.
Combine
1
3
and
u
3
.
1
3
⋅
u
3
3
+
C
Multiply
1
3
and
u
3
3
.
u
3
3
⋅
3
+
C
Multiply
3
by
3
.
u
3
9
+
C
Replace all occurrences of
u
with
3
x
+
4
.
(
3
x
+
4
)
3
9
+
C
Reorder terms.
1
9
(
3
x
+
4
)
3
+
C
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